##  [Integral Closure](/integral-closure) 

  ##  [Integral Closure](https://algebra.quantumdictionary.io/integral-closure-0) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The subobject obtained by adjoining to a given subring (or subalgebra) all elements of a containing ring that satisfy a monic polynomial with coefficients in the subring; equivalently, the set of elements integral over the subring.